Applying the new implication operator to professional judgement in risk assessment

The article describes a novel implication operator based on fuzzy entailment. Previously, (J. Daams, 1999) the operator was used for inference from a single rule and a single input. The paper describes how the operator would be used in an expert system. The operator is therefore extended to systems with multiple rules; to chained rules; to quantified rules; and to multidimensional input. If the rule set is incomplete, interpolation can be used, even when the rules are very sparse. By means of weighting or other manipulation of the multidimensional inputs, the new operator reproduces commonly used fuzzy logic techniques such as compensation. Missing rules and missing, dubious or contradictory inputs all broaden the envelope of plausible outcomes surrounding the interpolated conclusion, and reduce belief in this interpolated conclusion. The ability of the operator to calculate a plausible conclusion despite missing rules or data makes it suitable for process control and decision making. A software program customized for financial auditing is used to illustrate the practical aspects of the new fuzzy implication operator. The software mimics the informal reasoning which expert decision-makers use when exercising professional judgement, i.e., interpolating or extrapolating from sketchy, ambiguous, qualitative opinions, using a few experience based rules-of-thumb.